We report zero-field muon-spin rotation and relaxation measurements on the superconducting ferromagnet UCoGe. Weak itinerant ferromagnetic order is detected by a spontaneous muon-spin precession frequency below the Curie temperature T_C = 3  K. The μ+ precession frequency persists below the bulk superconducting transition temperature T_sc = 0.5  K, where it measures a local magnetic field B_loc = 0.015  T. The amplitude of the μSR signal provides unambiguous proof for ferromagnetism present in the whole sample volume. We conclude ferromagnetism coexists with superconductivity on the microscopic scale.